CF2082A Binary Matrix

A matrix is called binary if all its elements are either $ 0 $ or $ 1 $ . Ecrade calls a binary matrix $ A $ good if the following two properties hold: - The [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all numbers in each row of matrix $ A $ is equal to $ 0 $ . - The [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all numbers in each column of matrix $ A $ is equal to $ 0 $ . Ecrade has a binary matrix of size $ n \cdot m $ . He is interested in the minimum number of elements that need to be changed for the matrix to become good. However, it seems a little difficult, so please help him!

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 400 $ ). The description of the test cases follows. The first line of each test case contains two integers $ n, m $ ( $ 1 \le n, m \le 100 $ ). This is followed by $ n $ lines, each containing exactly $ m $ characters consisting only of $ 0 $ and $ 1 $ , describing the elements of Ecrade's matrix. It is guaranteed that the sum of $ n \cdot m $ across all test cases does not exceed $ 5 \cdot 10^4 $ .

For each test case, output a single integer, the minimum number of elements that need to be changed.

In the first test case, he needs to change 2 elements to obtain the following matrix $ \begin{pmatrix}1&1&0\\1&0&1\\0&1&1\end{pmatrix} $ . In the second test case, he can make no changes to obtain the following matrix $ \begin{pmatrix}0&0&0\\0&0&0\\0&0&0\end{pmatrix} $ . In the third test case, he needs to change 3 elements to obtain the following matrix $ \begin{pmatrix}1&0&1\\0&0&0\\1&0&1\end{pmatrix} $ .